Decoding-based method for quantum circuit optimization

1. A method for synthesizing a quantum circuit comprising the steps of:

a. Determining an ordered set or vector of phase coefficients,

b. Specifying a linear permutation,

c. Determining a sequence of CNOT and R Z gates using the set of phase coefficients and the linear permutation, such that the number of R Z gates is minimized.

2. The method of claim 1 , further comprising the step of:

a. Replacing said first set of phase coefficients with a second set of phase coefficients, wherein the first set of phase coefficients and the second set of phase coefficients represent the same quantum operation,

b. reducing the number of R Z gates required.

3. The method of claim 2 , further comprising the use of a decoding algorithm to determine said second set of phase coefficients.

4. A method for optimizing a quantum circuit, expressed as a sequence of CNOT and R Z gates, wherein the circuit is first analyzed to obtain a set of phase coefficients and a linear permutation, and then the method of claim 1 is utilized to synthesize a new circuit.

5. The method of claim 4 , wherein a Reed-Muller decoding method is utilized to determine an alternate set of phase coefficients minimizing the number of R Z gates required.

6. The method of claim 5 , wherein the Reed-Muller decoder is used to decode the binary residue of the set of phase coefficients, the result of which is then used to generate the alternate set of phase coefficients.

7. The implementation of the method of claim 4 as a computer program, wherein a processor receives a quantum circuit expressed over CNOT and R Z gates in suitable digital form, and then produces an optimized circuit in suitable digital form performing the same function.

8. A non-transitory computer readable medium for synthesizing a new quantum circuit, the non-transitory computer readable medium comprising computer executable instructions according to the method of claim 4 .

9. A computing system for optimizing a quantum circuit, comprising:

a memory device that stores a first digital form of an initial quantum circuit expressed as a sequence of CNOT and R Z gates;

a processor device that obtains and analyzes the first digital form to determine an ordered set or vector of phase coefficients and to specify a linear permutation;

the processor device determines a sequence of CNOT and R Z gates using the set of phase coefficients and the linear permutation, such that the number of R Z gates is reduced;

the processor device subsequently computes a second digital form of a new quantum circuit; and

the memory devices stores the second digital form.

10. A process of producing a quantum circuit, comprising:

obtaining a digital form of an initial n-qubit quantum circuit expressed over CNOT and R Z gates;

a computer analyzing the digital form of the initial quantum circuit to obtain a set of phase coefficients and a linear permutation;

the computer determining a sequence of CNOT and R Z gates using the set of phase coefficients and the linear permutation, and computing a digital form of a new n-qubit quantum circuit from the sequence having a reduced number of R Z gates compared to the initial quantum circuit, and the new quantum circuit performing the same function as the initial quantum circuit; and

executing physical CNOT and R Z transformations in a quantum computer in accordance with the digital form of the new quantum circuit.

11. A system of producing a quantum circuit, comprising:

a binary computer in data communication with a quantum computer;

the binary computer comprising a memory device that stores a digital form of an initial n-qubit quantum circuit expressed over CNOT and R Z gates;

the binary computer comprising a processor device to:

analyze the digital form of the initial quantum circuit to obtain a set of phase coefficients and a linear permutation;

determine a sequence of CNOT and R Z gates using the set of phase coefficients and the linear permutation, and compute a digital form of a new n-qubit quantum circuit from the sequence having a reduced number of R Z gates compared to the initial quantum circuit, and the new quantum circuit performing the same function as the initial quantum circuit;

the binary computer further comprising a communication device to transmit the digital form of the new quantum circuit to the quantum computer;

the quantum computer comprising a communication device to receive the digital form of the new quantum circuit; and

the quantum computer comprising devices to execute physical CNOT and R Z transformations in the quantum computer in accordance with the digital form of the new quantum circuit.